Question 1003625

We are doing systems of nonlinear equations in two variables. So solving with either the addition method or substitution method. The problem is solve the systems log x^2=y+3 log x=y-1. I don't know what to do with the logs. If the logs were not there I would solve with the substitution method, I would solve for y in x=y-1,y=x+1. Plug that into the x^2 problem. A log is log 10^1. I'm stuck. 
<pre>{{{log (x^2) = y + 3 }}}
{{{10^(y + 3) = x^2}}} ----------- Converting to EXPONENTIAL form -------- eq (i)

{{{log x = y - 1}}}
{{{10^(y - 1) = x}}} ------------- Converting to EXPONENTIAL form --------- eq (ii)

{{{10^(y + 3) = (10^(y - 1))^2}}} ------ Substituting {{{10^(y - 1)}}} for x in eq (i) 
{{{10^(y + 3) = 10^(2y - 2)}}}
y + 3 = 2y – 2 ----------- Bases are equal and so are the exponents
y – 2y = - 2 – 3
- y = - 5
y = {{{(- 5)/(- 1)}}}, or 5

{{{10^(5 - 1) = x}}} --------- Substituting 5 for y in eq (ii) 
{{{10^4 = x}}}, or x = 10,000

Solution set: {{{highlight_green(system(x = 10000,y =5))}}}